I'm pushing 280k miles on my '87 325e that is all original, never rebuilt. I know nothing about the reliability specific to the iX (they are rare cars), but for the most part, e30 BMWs are pretty solid cars. The engines are great - they will last a LONG time with just simple routine oil changes and timing belt changes.
Timing belts should be changed every 60k miles. If it breaks, it's bad. Water pumps are EASY to replace and are about $50 for the part via the internet. If you are replacing the timing belt and you are unsure of the age of the water pump, go ahead and do the water pump at the same time - there won't be any additional labor to do it.
The service light that is on on the dash is probably the "Inspection" light. These cars have inspection schedules that you can learn lots about with a simple google search. They are usually very pricey if done at the dealer, but they don't really do anything that you can't do yourself cheaply - they mostly entail just replacing fluids and examining the conditions of various critical parts to assess for wear.
No matter what you have read in other forums, the e30 automatic transmission is a weak point in the car. BMW automatics have always been and continue to be weak points even in the brand new cars. No, not all of them crap out at 120,000 miles, but many of them do. It's just something to be aware of, because your car may be one of the ones where it does crap out at 120,000. You WILL be replacing the automatic at some point, because I can guarantee you that it won't last as long as the engine. If the car is a manual (which I assume it isn't since you got defensive when told that the automatics don't last as long), the clutch will last over 200k if not beat to hell (my original clutch lasted 260k) and cost between $400-600 to replace. That's much cheaper than the replacement of an automatic transmission.
Another common problem is the steering racks - they often will crap out at a little over 100k. I have 280k on my original one, but that is definitely the exception, not the rule.
The A/C system can get expensive to repair if/when it breaks. The compressors used on most of the e30s (Nippondensos) are very expensive to replace and are known for their tendency to sieze. The expansion valve is another common part to have to replace.
Lots of people seem to have problems with the electrical system in these cars, but I haven't really had much issue with mine.
Parts usually aren't too expensive for these cars - you can save a lot of money by ordering parts online unless you have a cool local BMW dealer that will match mail order prices on parts. There are a few parts here and there that are overly expensive for what the part is. For the most part, these are pretty simple cars and are usually pretty easy to work on. Alot of the jobs "require" a special BMW tool, but you can usually do the job without it. You said you aren't mechanically inclined, so that really doesn't matter anyways. If you are going to be paying someone to work on the car, beware that this can get very expensive in the US - most of your BMW specialists are expensive.
Like I said, I know nothing about the reliability of the iX specific parts since they are so rare, but I have read that replacing the AWD system parts can be expensive. Also keep in mind that other suspension parts (struts, control arms, etc) are different from the much much more common non-AWD cars and are therefore more expensive as well.
Problem areas: the automatic transmissions (whether you want to admit it or not), timing belts, water pumps, driveshaft flex discs, driveshaft center support bearing, transmission output shaft seal leaks on the manuals, wheel bearings on higher mile cars, seat heaters, rear tailight gaskets leaking (easy fix), rear shock mounts, service interval circuit board batteries, power steering racks, fuel pumps, odometer gears breaking, windshields pitting, Nippondenso A/C compressors siezing. The driveshaft flex disk and center support bearings are especially commonly replaced parts - my CSB just crapped out on me day before yesterday, so I am driving a rental car until I can tear the damn thing apart and fix it this weekend.
It'd be worth $50-$60 to take the car to a BMW specialist to have them inspect it before purchasing.
